List of basic mathematics topics

Mathematics is the search for fundamental truths in pattern, quantity, and change. For more on the relationship between mathematics and science, refer to the article on science.

The following outline is provided as an overview of and introduction to mathematics:

Subjects of mathematics

Quantity

: "Main article: Quantity"

* Natural numbers
* Integers
* Rational numbers
* Real numbers
* Complex numbers

Structure

: "Main article: Structure"

* Number theory
* Abstract algebra
* Order theory

Space

: "Main article: Space"

*Geometry
* Trigonometry
* Differential geometry
* Topology
* Fractal geometry

Change

: "Main article: Change"

* Calculus
* Vector calculus
* Differential equations
* Dynamical systems
* Chaos theory

Foundations and philosophy

* Philosophy of mathematics
* Category theory
* Set theory

Mathematical logic

* Model theory
* Proof theory
* Recursion theory
* Set theory

Discrete mathematics

* Combinatorics
* Theory of computation
* Cryptography
* Graph theory

Applied mathematics

* Mathematical physics
* Analytical mechanics
* Mathematical fluid dynamics
* Numerical analysis
* Optimization
* Probability
* Statistics
* Mathematical economics
* Financial mathematics
* Game theory
* Mathematical biology
* Cryptography
* Operations research
* Information theory
* Control theory
* Dynamical systems

History of mathematics

: "Main article: History of mathematics"
*Babylonian mathematics
*Egyptian mathematics
*Indian mathematics
*Greek mathematics
*Chinese mathematics
**Abacus
*History of the Hindu-Arabic numeral system
*Islamic mathematics
*Japanese mathematics
*History of algebra
*History of geometry
*History of mathematical notation
*History of trigonometry
*History of writing numbers

Basic mathematics concepts

Algebra -- Analysis -- Area -- Arithmetic -- Calculus -- Category theory -- Combinatorics -- Complex number -- Computation -- Coordinate system -- Decimal -- Derivative -- Digit -- Equation -- Fractal -- Function (mathematics) -- Geometry -- Infinity -- Integral -- Length -- Limit -- Logarithm -- Logic -- Matrix -- Number -- Numeral -- Pi -- Power -- Prime number -- Proof -- Rational number -- Real number -- Series -- Set -- Trigonometry -- Vector space -- Vector (geometric) -- Volume

Influential mathematicians

*Bartel Leendert van der Waerden
*Leonhard Euler
*Pythagoras
*Fibonacci

Mathematics lists

: "Main article: Lists of mathematics topics"

External links

* Online Encyclopaedia of Mathematics [http://eom.springer.de] from Springer. Graduate-level reference work with over 8,000 entries, illuminating nearly 50,000 notions in mathematics.
* [http://www-math.mit.edu/daimp Some mathematics applets, at MIT]
* Rusin, Dave: [http://www.math-atlas.org/ "The Mathematical Atlas"] . A guided tour through the various branches of modern mathematics. (Can also be found [http://www.math.niu.edu/~rusin/known-math/index/index.html here] .)
* Stefanov, Alexandre: [http://us.geocities.com/alex_stef/mylist.html "Textbooks in Mathematics"] . A list of free online textbooks and lecture notes in mathematics.
* Weisstein, Eric et al.: [http://mathworld.wolfram.com/ "Wolfram MathWorld: The Web's Most Extensive Mathematics Resource"] . An online encyclopedia of mathematics.
* Polyanin, Andrei: [http://eqworld.ipmnet.ru/ "EqWorld: The World of Mathematical Equations"] . An online resource focusing on algebraic, ordinary differential, partial differential (mathematical physics), integral, and other mathematical equations.
* [http://planetmath.org/ "Planet Math"] . An online mathematics encyclopedia under construction, focusing on modern mathematics. Uses the GFDL, allowing article exchange with Wikipedia. Uses TeX markup.
* [http://metamath.org/ "Metamath"] . A site and a language, that formalize mathematics from its foundations.
* [http://www-history.mcs.st-and.ac.uk/~history/ Mathematician Biographies] . The MacTutor History of Mathematics archive Extensive history and quotes from all famous mathematicians.
* Cain, George: [http://www.math.gatech.edu/~cain/textbooks/onlinebooks.html Online Mathematics Textbooks] available free online.
* [http://etext.lib.virginia.edu/DicHist/analytic/anaVII.html Math & Logic: The history of formal mathematical, logical, linguistic and methodological ideas.] In "The Dictionary of the History of Ideas."
* [http://www.nrich.maths.org/public/index.php Nrich] , a prize-winning site for students from age five from Cambridge University
* [http://www.freescience.info/mathematics.php 'FreeScience Library->Mathematics '] The mathematics section of FreeScience library
* [http://garden.irmacs.sfu.ca Open Problem Garden] , a wiki of open problems in mathematics
* [http://www.mathmotivation.com/all-applications.html Applications of High School Algebra]